( d ) y d n ) = x ( n 2 - 2n

Code128 Scanner In NoneUsing Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications.

Code 128 Code Set B Maker In NoneUsing Barcode generator for Software Control to generate, create Code 128C image in Software applications.

+ 1)

Read Code 128 In NoneUsing Barcode reader for Software Control to read, scan read, scan image in Software applications.

Make Code 128C In C#Using Barcode maker for .NET Control to generate, create ANSI/AIM Code 128 image in VS .NET applications.

CHAP. 11

Painting Code-128 In .NET FrameworkUsing Barcode maker for ASP.NET Control to generate, create Code-128 image in ASP.NET applications.

Drawing Code 128 Code Set B In .NETUsing Barcode printer for Visual Studio .NET Control to generate, create Code 128B image in .NET framework applications.

SIGNALS AND SYSTEMS

Generating Code 128A In Visual Basic .NETUsing Barcode creator for .NET framework Control to generate, create Code 128 image in VS .NET applications.

Print UPC - 13 In NoneUsing Barcode encoder for Software Control to generate, create EAN / UCC - 13 image in Software applications.

(a) The sequence x(n), illustrated in Fig. 1-8(a), a linearly decreasing sequence that begins at index n = 0 and is ends at index n = 5. The first sequence that is to be sketched, yl(n) = x(4 - n), is found by shifting x(n) by four and time-reversing. Observe that at index n = 4, yl(n) is equal to x(0). Therefore, yl(n) has a value of 6 at n = 4 and decreases linearly to the left (decreasing values of n) until n = - 1, beyond which y (n) = 0.The sequence y (n) is shown in Fig. 1-8(b).

Bar Code Creation In NoneUsing Barcode encoder for Software Control to generate, create barcode image in Software applications.

Data Matrix ECC200 Encoder In NoneUsing Barcode creator for Software Control to generate, create DataMatrix image in Software applications.

Fig. 1-8. Performing signal manipulations.

Draw Barcode In NoneUsing Barcode encoder for Software Control to generate, create barcode image in Software applications.

USS-128 Drawer In NoneUsing Barcode encoder for Software Control to generate, create GS1 128 image in Software applications.

(b) The second sequence, y2(n) = x(2n - 3), is formed through the combination of time-shifting and downsampling. Therefore, y&~) may be plotted by first shifting x(n) to the right by three (delay) as shown in

International Standard Book Number Generator In NoneUsing Barcode creation for Software Control to generate, create ISBN - 13 image in Software applications.

Draw Data Matrix 2d Barcode In JavaUsing Barcode printer for Android Control to generate, create ECC200 image in Android applications.

SIGNALS AND SYSTEMS

Barcode Creator In C#Using Barcode generator for .NET Control to generate, create barcode image in .NET applications.

EAN13 Generator In .NETUsing Barcode drawer for ASP.NET Control to generate, create EAN-13 image in ASP.NET applications.

[CHAP. 1

Code 3/9 Decoder In NoneUsing Barcode recognizer for Software Control to read, scan read, scan image in Software applications.

Read Bar Code In JavaUsing Barcode Control SDK for BIRT Control to generate, create, read, scan barcode image in BIRT applications.

Fig. 1-8(c). The sequence y2(n) is then formed by down-sampling by a factor of 2 (i.e., keeping only the even index terms as indicated by the solid circles in Fig. 1-8(c)). A sketch of yn(n) is shown in Fig. I-8(d). (c) The third sequence, y3(n) = x(8 - 3n), is formed through a combination of tirne-shifting, down-sampling, and time-reversal. To sketch y3(n) we begin by plotting x(8 - n), which is formed by shifting x(n) to the left by eight (advance) and reversing in time as shown in Fig. 1 -8(e). Then, y3(n) is found by extracting every third sample of x(8 - n), as indicated by the solid circles, which is plotted in Fig. 1-8(f ) .

Generate Code39 In JavaUsing Barcode creation for Java Control to generate, create Code-39 image in Java applications.

Reading Universal Product Code Version A In Visual C#.NETUsing Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.

(4 Finally, y4(n) = x(n2 - 2n + 1) is formed by a nonlinear transformation of the time variable n. This sequence

may be easily sketched by listing how the index n is mapped. First, note that if n 2 4 or n 5 -2, then n2 - 2n + 1 2 9 and, therefore, y4(n) = 0. For - I 5 n 5 3 we have

The sequence y4(n) is sketched in Fig. 1-8(g).

The notation ~ ( ( n ) is ~ ) used to define the sequence that is formed as follows: ~ ( ( n ) = ~ modulo N) ) x(n where (n modulo N) is the positive integer in the range [0, N - 11 that remains after dividing n by N. For example, ((3))g = 3, ((12))g = 4, and ((-6))d = 2. If x(n) = (i)%in(nn/2)u(n), make a sketch of (a) x((n))3 and (b)x((n - 2))3.

(a) We begin by noting that ((n))3, for any value of n, is always an integer in the range [O, 21. In fact, because ((n))3 = ((n 3k)h for any k ,

Therefore, x((n))3 is periodic with a period N = 3. It thus follows t h a t ~ ( ( n )is~ ) formed by periodically repeating the first three values of x(n) as illustrated in the figure below:

(b) The sequence x((n - 2))3 is also periodic with a period N = 3, except that the signal is shifted to the right by no = 2 compared to the periodic sequence in part (a). This sequence is shown in the figure below:

The power in a real-valued signal x(n) is defined as the sum of the squares of the sequence values:

Suppose that a sequence x(n) has an even part x,(n) equal to

CHAP. I]

SIGNALS AND SYSTEMS

If the power in x(n) is P = 5, find the power in the odd part, x,(n), of x(n).

This problem requires finding the relationship between the power in x ( n ) and the power in the even and odd parts. By definition, x ( n ) = x , ( n ) x,(n). Therefore,

Note that x,(n)x,(n) is the product of an even sequence and an odd sequence and, therefore, the product is odd. Because the sum for all n of an odd sequence is equal to zero,